Abstract

A discussion of the stability of self-gravitating Skyrmions, with a large winding number N, in a Schwarzschild type of metric, is presented for the case where an isospin chemical potential is introduced. It turns out that the chemical potential stabilizes the behavior of the Skyrmion discussed previously in the literature. This analysis is carried on in the framework of a variational approach using different ansatze for the radial profile of the Skyrmion. We found a divergent behavior for the size of the Skyrmion, associated to a certain critical value μc of the chemical potential. At this point, the mass of the Skyrmion vanishes. μc is essentially independent of gravitating effects. The stability of a large N skyrmion against decays into single particles is also discussed. © World Scientific Publishing Company.